Jack has a test with a total of 15 questions. He has to answer 12 of these questions.
In how many ways can he choose which questions to answer if he at least has to choose 3 out of the 5 first questions?
Thank you for taking the time to read my post.
He must answer 3, 4, or 5 out of the first 5 questions.
If he answers 3 out of the first 5 then he must answer 9 out of the last 10; if he answers 4 out of the first 5 then he must answer 8 out of the last 10; and if he answers 5 out of the first 5 then he must answer 7 out of the last 10.
So the total number of possibilities is
.
Thank you both for taking the time to respond to my thread.
I also thought that if he has to choose atleast 3 out of the first five questions he had to do as you said, but that is counter intuitive to me, let me explain why:
.
Sorry, at further analysis I come to understand that neither a, b or c hold any identical combination of which questions he chose to answer. I appreciate your help.